Data integrity verification (DIV) is one of the primary security checks for data stored on cloud servers. Cloud users have assured the safety of their data with frequent checking of data integrity. In this paper, we provide an efficient and effective DIV approach that offers effective and privacy-preserving audit structure.The main building components of our approach are a multi-power variant of the Paillier cryptography system with homomorphic tag. The Paillier cryptography system along with homomorphic tag assigns a unique and verifiable value to each data block, which helps performing dynamic data operations in cloud environment. To demonstrate our approach, we have implemented an application on Hadoop and MapReduce framework. We have tested this application with respect to the different parameters. The efficiency of the proposed method hasbeen shown through the experimental results. Our method has shown a good improvement over those of the other modern systems.